Hybrid vibration control by piezolelectrics with the optimal resistance and the optimal control theory

摘要

This paper proposes the use of the optimal resistance and LQ optimum contorl theory as the method of designing the active-passive hybrid vibration control of structures. Previous studies have shown that piezoleelctric materials convenrt mechanical energy into electricla energy, and this electrical energy may be dissipated maximally through a connected optimal resistance. used in conjunction with an active control circuit to the optimal resistance, the hybrid control can be applied, which combines the advantages of passive and active control. In the other words, the optimal resistance provides passive damping to the structure, while the LQ controller improvesthe performance of the passive control system. However, fail-safe is always guaranteed for the hybrid control system by the passive damping. To apply the LQ control thoey, state space models of the coupling system of structure with piezolelectric elements and resistances are formulated. The state space model cescribes the dynamic coupling between a structure and resistances through the pizoelectric effect. Therefore, its active control formula can be obtaiend in a very simple manner. Lastly, the theoretical calculation of a cantilevered beam is carried out to demonstrate the effectiveness of the concept.